In the community of topology optimization, the contradiction between the frontier research with structured meshes and the complex geometry in the real-world problems has existed for a long time. Structured mesh is attractive in convenient application of loads and boundary conditions, and easy implementation of GPU parallel calculation. Therefore, unlike existing researches solving the issue through unstructured elements, this paper presents an easy-to-accomplish virtual phase method (VPM) based on structured meshes, to systematically solve the problems with complex geometries and arbitrary non-design domains. Structural geometry is denoted by the extended regular design domain and void region initially placed at the border of the extended domain. Based on the extended idea of composite material interpolation in multi-phase density-based topology optimization approaches, the extended structural design domains and the pre-defined non-design domains are considered as the optimized phases in the structure, and they are defined by discrete variable fields. Subsequently, the structural optimization is implemented like as the traditional multi-material topology optimization process. Numerical examples accounting for minimum compliance are presented to demonstrate the effectiveness of the proposed method, including multi-phase macrostructural design, the ease with which the method can accommodate passive regions, and how the length scale constraints are used to devise graded porous infill morphology within a given shell. At last, the manufacturability of the optimized designs is discussed to further verify the applicability of the proposed method. Our approach provides those front researches based on structured meshes with an easily accessible access, to be straightforwardly applied for any complex-domain design problem.

在拓扑优化社区中，结构化网格的前沿研究与现实世界问题中的复杂几何之间的矛盾由来已久。结构化网格在载荷和边界条件的方便应用以及GPU易于实现方面具有吸引力并行计算。因此，与现有研究通过非结构化单元解决问题不同，本文提出了一种基于结构化网格的易于实现的虚拟相法（VPM），以系统地解决具有复杂几何形状和任意非设计域的问题。结构几何由扩展的规则设计域和最初放置在扩展域边界的空隙区域表示。基于多相密度拓扑优化方法中复合材料插值的扩展思想，扩展的结构设计域和预定义的非设计域被视为结构中的优化相，它们由离散变量字段。随后，结构优化的实施与传统的多材料拓扑优化过程一样。给出了考虑最小合规性的数值例子，以证明所提出方法的有效性，包括多相宏观结构设计，该方法可以轻松适应被动区域，以及如何使用长度尺度约束来设计梯度多孔填充形态。给定的外壳。最后，产品的可制造性讨论了优化设计以进一步验证所提出方法的适用性。我们的方法为那些基于结构化网格的前沿研究提供了一个易于访问的方法，可以直接应用于任何复杂领域的设计问题。